One important task in image processing is noise reduction, which requires to recover image information by removing noise without loss of local structures. In recent decades patch-based denoising techniques proved to have a better performance than pixel-based ones, since a spatial neighbourhood can represent high correlations between nearby pixels and improve the results of similarity measurements. This bachelor thesis deals with denoising strategies with patch-based principal component analysis. The main focus lies on learning a new basis on which the representation of an image has the best denoising effect. The first attempt is to perform principal component analysis on a global scale, which obtains a basis that reflects the major variance of an image. The second attempt is to learn bases respectively over patches in a local window, so that more image details can be preserved. In addition, local pixel grouping is introduced to find similar patches in a local window. Due to the importance of sufficient samples in the principal component analysis transform, the third attempt is to search for more similar patches in the whole image by using a vantage point tree for space partitioning. In the part of implementation, parameter selection and time complexity are discussed. The denoising performance of different approaches is evaluated in terms of both PSNR value and visual quality.